Computing in the dark sector: a Cactus toolkit for modified-gravity cosmologies (Marie Curie International Reintegration Grant #PIRG05-GA-2009- 249290)

In technical terms, COSMOTOOLKIT aims at designing, extending, and testing the community infrastructure of numerical relativity, contained in the Einstein Toolkit, to tackle physical questions of cosmological interest and bring the full power of high-performance computing to relatistic cosmology.

A question that has kept resurfacing in recent years is: does large-scale cosmology require a full, multi-scale relativistic treatment? General relativity is well studied in the isolated-object regime, which applies, for instance, to galaxies (which typically extend over a few kiloparsecs), and in the large-scale, statistically homogeneous regime, which is appropriate for the regions of the universe larger than a few Gigaparsecs; general relativistic effects in these two regimes, however, are assumed not to talk to each other across the scales that separate them. In other words, one uses relativistic building blocks to construct a relativistic large-scale structure, but the way in which this structure is assembled is assumed to be almost exactly Newtonian.

The legitimacy of this approach is not so much rooted in an accurate study of the relativistic effects in the intermediate regime (a study of formidable computational complexity), as in the observational fact that the model deriving from this assumption reproduces the observations quite well. This result, however, comes at a price: the fits also indicate that over 95% of the energy density in the universe is provided by two components, dark energy and dark matter, of an as of yet unknown nature. It can be safely estimated that the dark sector is the most active field of cosmology today.

Filling this scale gap in our picture of the universe is thus not merely an academic exercise: over the past couple of decades, science agencies worldwide have invested the equivalent of several billions of Euros for space missions aimed to measure some of the elusive properties of our universe, resulting in an unprecedented level of insight into the origin, evolution and fate of our cosmic habitat. Nonetheless, the new data has also opened up new questions, which can only be answered by refinining the observations and developing detailed theoretical scenarios to frame them. The era of precision cosmology does not only involve precision data, but also a corresponding effort in precision modelling to correctly interpret these data.

Whilst the modelling of compact objects has witnessed tremendous progress over the past two decades, both for the study of the strong-gravity regime (where potential deviations from General Relativity would be largest) and for the detection of gravitational waves, the development of a full-3D relativistic cosmology is lagging behind. The description of crucial phenomena like the generation and the evolution of the seeds of cosmic structures are still limited to the perturbative regime, and the use of cosmological data to test the validity of General Relativity is still in its infancy.

COSMOTOOLKIT aims at contributing to the modelling effort through numerics. Full relativistic-hydrodynamics simulations of the large-scale universe would illustrate the magnitude and properties of the non-linear effects in a cosmological spacetime, and thereby assess the regime of validity of perturbation theory. Access to the non-linear regime would amplify modified-gravity effects and guide the search for these effects in the wealth of cosmological data available today. Gravitational-wave signatures of deviations from General Relativity are also within COSMOTOOLKIT's scope and its planned infrastructure extensions.

COSMOTOOLKIT's cycle started in June 2010 with an intense burst of code development, leading to the creation of the Cosmology suite, a collection of tools for the evolution of fluids such as cosmic dust and scalar fields, the generation of initial data and the analysis of the simulation data. These tools are based on state-of-the-art techniques such as automated code generation. The suite has only been distributed to a number of test users so far, but will be publicly distributed as a component of the Einstein Toolkit by the time COSMOTOOLKIT's cycle ends.

In addition to the new Cosmology suite, COSMOTOOLKIT has also contributed to the development of existing components of the Einstein Toolkit.

In several cases, fundamental issues with the problem formulation had to be resolved before a numerical effort could be devised. In parallel with the infrastructure development, and in collaboration with experts in mathematical relativity and cosmology, COSMOTOOLKIT's focus has also come to include topics such as the existence and uniqueness of solutions on spacetimes that are spatially periodic, the choice of coordinate gauges in a non-asymptotically-flat spacetime, and the construction of periodic black-hole lattices. These may be regarded as the simplest GR solutions encompassing large-scale homogeneity and small-scale inhomogeneity; whilst these solutions were sought after for over fifty years, it was only within COSMOTOOLKIT that the first complete evolution was carried out and analyzed, unveiling the lattice's surprising behavior and opening an abundance of questions for analytical and numerical researchers alike.

Due to the deep connection of numerical modelling with parameter estimation, COSMOTOOLKIT also has a data-analysis component with the goal of creating an analysis package for parameter estimation and model selection within generic cosmological models.